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A306026
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Antidiagonal sums of A306024.
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3
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1, 1, 2, 5, 16, 66, 343, 2180, 16505, 145773, 1477880, 16986349, 219158316, 3147962668, 49982588535, 871766923048, 16609804758449, 344016348602845, 7711752589539436, 186379711851775401, 4839449174872615116, 134575228738532130948, 3996183953610068510929
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n} j! * [x^j] exp(Sum_{i=1..n-j} (exp(i*x)-1)/i).
a(n) = Sum_{j=0..n} A306024(j,n-j).
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MAPLE
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b:= proc(n, k, m) option remember; `if`(n=0, 1,
add(b(n-1, k, max(m, j)), j=1..m+k))
end:
a:= n-> add(b(j, n-j, 0), j=0..n):
seq(a(n), n=0..25);
# second Maple program:
b:= (n, k)-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..k)), x, n+1), x, n):
a:= n-> add(b(j, n-j), j=0..n):
seq(a(n), n=0..25);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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